Efficient Orthogonal Precoding to Simultaneously Suppress OOBE and Peak Power of OFDM Signals via Trapezoidal Block Householder Reflector

This study proposes a trapezoidal block Householder reflector (TBHR) as a storage-efficient solution for orthonormalization, and thereby, a practical scheme of orthogonally spectral precoding named the TBHR orthogonally precoded discrete Fourier transform spread orthogonal frequency-division multiplexing (TBHR-OP-DFT-s-OFDM) to simultaneously resolve the two major problems of high out-of-band emission (OOBE) and peak power characteristics of OFDM signals in dynamic spectrum access. TBHR has noteworthy properties similar to orthogonal projection and Moore–Penrose pseudo inverse matrix, including the norm minimality related to the optimal solution to a specific orthogonal Procrustes problem. With TBHR, TBHR-OP-DFT-s-OFDM can concurrently achieve practical performances to realize spectrum sharing in dynamic spectrum access, such as effective OOBE suppression, practical peak power suppression, ideal error rate characteristics, and efficient computational complexity.